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Borda and the maximum likelihood approach to vote aggregation

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  • Truchon, Michel

Abstract

Drissi-Bakhkhat and Truchon ["Maximum Likelihood Approach to Vote Aggregation with Variable Probabilities," Social Choice and Welfare, 23, (2004), 161-185.] extend the Condorcet-Kemeny-Young maximum likelihood approach to vote aggregation by relaxing the assumption that the probability of correctly ordering two alternatives is the same for all pairs of alternatives. They let this probability increase with the distance between the two alternatives in the true order, to reflect the intuition that a judge or voter is more prone to errors when confronted to two comparable alternatives than when confronted to a good alternative and a bad one. In this note, it is shown than, for a suitably chosen probability function, the maximum likelihood rule coincides with the Borda rule, thus, partially reconciling the Borda and the Condorcet methods.
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  • Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
    • Handle: RePEc:eee:matsoc:v:55:y:2008:i:1:p:96-102
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    1. Mohamed Drissi-Bakhkhat & Michel Truchon, 2004. "Maximum likelihood approach to vote aggregation with variable probabilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 161-185, October.
    2. Donald Saari, 2006. "Which is better: the Condorcet or Borda winner?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 107-129, January.
    3. Mathias Risse, 2005. "Why the count de Borda cannot beat the Marquis de Condorcet," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 95-113, October.
    4. Michel Truchon, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0414, CIRPEE.
    5. Young, H. P., 1988. "Condorcet's Theory of Voting," American Political Science Review, Cambridge University Press, vol. 82(4), pages 1231-1244, December.
    6. Condorcet, Marquis de, 1793. "Esquisse d'un tableau historique des progrès de l'esprit humain," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number condorcet1793.
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    Cited by:

    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    3. Conitzer, Vincent, 2012. "Should social network structure be taken into account in elections?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 100-102.
    4. Jean-François Laslier, 2010. "In Silico Voting Experiments," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 311-335, Springer.
    5. Boudreau, James & Ehrlich, Justin & Sanders, Shane & Winn, Adam, 2014. "Social choice violations in rank sum scoring: A formalization of conditions and corrective probability computations," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 20-29.
    6. James Boudreau & Justin Ehrlich & Mian Farrukh Raza & Shane Sanders, 2018. "The likelihood of social choice violations in rank sum scoring: algorithms and evidence from NCAA cross country running," Public Choice, Springer, vol. 174(3), pages 219-238, March.
    7. Islam, Jamal & Mohajan, Haradhan & Moolio, Pahlaj, 2011. "Borda voting is non-manipulable but cloning manipulation is possible," MPRA Paper 50848, University Library of Munich, Germany, revised 10 Jan 2012.
    8. T. Tideman & Florenz Plassmann, 2014. "Which voting rule is most likely to choose the “best” candidate?," Public Choice, Springer, vol. 158(3), pages 331-357, March.
    9. Jung-Fa Tsai & Chin-Po Wang & Ming-Hua Lin & Shih-Wei Huang, 2021. "Analysis of Key Factors for Supplier Selection in Taiwan’s Thin-Film Transistor Liquid-Crystal Displays Industry," Mathematics, MDPI, vol. 9(4), pages 1-18, February.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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